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Fundamentals of Parameterized Complexity

  • Textbook
  • © 2013

Overview

Authors:
  1. Rodney G. Downey

    1. School of Mathematics, Statistics and Operations Research, Victoria University, Wellington, New Zealand

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    You can also search for this author in PubMed   Google Scholar

  2. Michael R. Fellows

    1. School of Engineering and Information Technology, Charles Darwin University, Darwin, Australia

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    You can also search for this author in PubMed   Google Scholar

  • Presents an accessible overview of the state of the art of multivariate algorithmics and complexity
  • Describes the wealth of recent techniques for proving parameterized tractability
  • Showcases the powerful new lower bound techniques
  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Computer Science (TCS)

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Table of contents (35 chapters)

  1. Front Matter

    Pages I-XXX
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  2. Parameterized Tractability

    1. Front Matter

      Pages 1-1
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    2. Preliminaries

      • Rodney G. Downey, Michael R. Fellows
      Pages 3-13

    3. The Basic Definitions

      • Rodney G. Downey, Michael R. Fellows
      Pages 15-21

  3. Elementary Positive Techniques

    1. Front Matter

      Pages 23-23
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    2. Bounded Search Trees

      • Rodney G. Downey, Michael R. Fellows
      Pages 25-47

    3. Kernelization

      • Rodney G. Downey, Michael R. Fellows
      Pages 49-89

    4. More on Kernelization

      • Rodney G. Downey, Michael R. Fellows
      Pages 91-106

    5. Iterative Compression, and Measure and Conquer, for Minimization Problems

      • Rodney G. Downey, Michael R. Fellows
      Pages 107-130

    6. Further Elementary Techniques

      • Rodney G. Downey, Michael R. Fellows
      Pages 131-141

    7. Color Coding, Multilinear Detection, and Randomized Divide and Conquer

      • Rodney G. Downey, Michael R. Fellows
      Pages 143-170

    8. Optimization Problems, Approximation Schemes, and Their Relation to FPT

      • Rodney G. Downey, Michael R. Fellows
      Pages 171-182

  4. Techniques Based on Graph Structure

    1. Front Matter

      Pages 183-183
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    2. Treewidth and Dynamic Programming

      • Rodney G. Downey, Michael R. Fellows
      Pages 185-203

    3. Heuristics for Treewidth

      • Rodney G. Downey, Michael R. Fellows
      Pages 205-211

    4. Methods via Automata and Bounded Treewidth

      • Rodney G. Downey, Michael R. Fellows
      Pages 213-264

    5. Courcelle’s Theorem

      • Rodney G. Downey, Michael R. Fellows
      Pages 265-278

    6. More on Width-Metrics: Applications and Local Treewidth

      • Rodney G. Downey, Michael R. Fellows
      Pages 279-289

    7. Depth-First Search and the Plehn–Voigt Theorem

      • Rodney G. Downey, Michael R. Fellows
      Pages 291-300

    8. Other Width Metrics

      • Rodney G. Downey, Michael R. Fellows
      Pages 301-316
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Keywords

About this book

This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.

Reviews

“It is a new book that conveys a detailed picture of parameterized complexity as it stands today. … The writing style is direct and engaging, allowing the reader to quickly grasp the core ideas for each topic. The book coverage is comprehensive, including even relatively recent results, and manages to give a rich representation of the current state of the field. In short, this is an excellent book that will serve well anyone interested in algorithm design and complexity.” (Marius Zimand, zbMATH 1358.68006, 2017)

“It can be read by graduate students who have some background in computational complexity. … I strongly recommend Fundamentals of Parameterized Complexity for all researchers in theoretical computer science. … It is my belief that this book is now the definitive text on parameterized complexity, both for the breadthand depth of material covered and also for including the latest developments in the field (as recently as 2012).” (Rajesh Chitnis, SIGACT News, Vol. 46 (1), 2015)

“This book is currently the only monograph that covers lower bounds in kernelization or parameterized approximation. … this new volume could serve as a (relatively easily) accessible source for a researcher in the area as well as helping students find their way into this interesting field. … nearly 700 citations and a well-designed index help to navigate through the book and through the literature.” (Henning Fernau, Mathematical Reviews, November, 2014)

Authors and Affiliations

  • School of Mathematics, Statistics and Operations Research, Victoria University, Wellington, New Zealand

    Rodney G. Downey

  • School of Engineering and Information Technology, Charles Darwin University, Darwin, Australia

    Michael R. Fellows

About the authors

Dr. Rodney G. Downey is a Professor in the School of Mathematics, Statistics and Operations Research, at the Victoria University of Wellington, New Zealand.

Dr. Michael R. Fellows is a Professor in the School of Engineering and Information Technology, at the Charles Darwin University, Darwin, NT, Australia.

Bibliographic Information

  • Book Title: Fundamentals of Parameterized Complexity

  • Authors: Rodney G. Downey, Michael R. Fellows

  • Series Title: Texts in Computer Science

  • DOI: https://doi.org/10.1007/978-1-4471-5559-1

  • Publisher: Springer London

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer-Verlag London 2013

  • Hardcover ISBN: 978-1-4471-5558-4Published: 17 December 2013

  • Softcover ISBN: 978-1-4471-7164-5Published: 27 August 2016

  • eBook ISBN: 978-1-4471-5559-1Published: 03 December 2013

  • Series ISSN: 1868-0941

  • Series E-ISSN: 1868-095X

  • Edition Number: 1

  • Number of Pages: XXX, 763

  • Number of Illustrations: 83 b/w illustrations

  • Topics: Algorithm Analysis and Problem Complexity, Mathematics of Algorithmic Complexity

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